CHOICE OF TIME SCALE FOR MODELING LONG-TERM SURVIVAL IN A COST-EFFECTIVENESS ANALYSIS: AN ILLUSTRATION

Purpose:

   To assess the influence of using chronological age as time scale instead of the conventional time-on-study time scale for modeling long-term survival within a cost-effectiveness analysis of total knee replacement (TKR).

Method:

   We used Osteoarthritis Initiative (OAI) data on 4354 subjects aged 45 to 79 without TKR at baseline with 7-year follow-up to develop the Knee OSteoarthritis MicrOSimulation (KOSMOS) model. Health states consisted of: Alive without TKR, Post TKR, and Dead. Instead of using the conventional time-on-study as the time scale, we fitted cause-specific, multivariable Cox regression models with TKR and death as competing events and chronological age as the time scale (KOSMOS-Age). Gender, race, education, body-mass index, knee injury/surgery, pain scores, and Kellgren-Lawrence radiographic grades were included as covariables. For illustrative purposes, the effect of TKR on quality of life was estimated using Short Form Health Survey data from before-after studies. Costs were estimated from a U.S. health system perspective. Mortality was calibrated to resemble life expectancy based on U.S. life tables. We subsequently simulated the virtual life course of an average knee osteoarthritis patient (mean age 61) until age 85 and estimated quality-adjusted life years (QALYs) and total costs for two scenarios: current practice and TKR at a 65% lower rate as observed before the procedure’s post-millennial increase. Outcomes predicted by KOSMOS-Age were compared with KOSMOS models fitted with a baseline age effect and time-on-study as time scale. In one version, cumulative hazards were extrapolated assuming a Weibull distribution (KOSMOS-Weibull). In a second version, we repeatedly reset the baseline cumulative hazard function’s time clock to zero after each seventh year with updating baseline covariables according to projected changes (KOSMOS-Updated). All KOSMOS models were refitted in 200 bootstrap datasets.

Result:

   The likelihood of undergoing a TKR in current vs past practice was 0.301 (95%CI 0.237-0.353) vs 0.121 (95%CI 0.091-0.144) as predicted by KOSMOS-Age, 0.419 (95%CI 0.303-0.559) vs 0.179 (95%CI 0.117-0.259) by KOSMOS-Weibull, and 0.342 (95%CI 0.295-0.389) vs 0.142 (95%CI 0.119-0.167) by KOSMOS-Updated. Current practice resulted in QALY gains of 0.236 using KOSMOS-Age, 0.362 using KOSMOS-Weibull, and 0.280 using KOSMOS-Updated, against increases in costs of $3717, $4857, and $4098 respectively. 

Conclusion:

   Cost-effectiveness outcomes may depend on the choice of time scale and method for modeling long-term survival. Decision modellers should consider this structural uncertainty.